th  - 1987 - 51st ENC Conference

MK3
OLIGONUCLEOTIDE STRUC'I13RE ~ BASED ON QUANTITATIVE 2DNOE SPECTRA
Brandan A. Borgias* and 'rnomas L. James
Department of Pharmaceutical Chemistry
Unive~ty of California, San Francisco, CA 94143
The use of 2DNOE (two-dimensional nuclear Overhauser effect) spectroscopy in the muc-
characterization of biomolecules has generally been qualitative or semi-quantitative.
Observed cross-peaks me presumed to be a consequence of the close proximity (< 5 ~,) for the
associated protons. Distances are estimated based on the relative intensifies and buildup of cross-
peaks according to an approximate relationship between the intensifies and the proton-proton dis-
tances. Distances obtained in this manner have proven useful as constraints in structural determi-
nations by distance geometry ! and molecular dynamics 2 calculations.
The exact relationship between the inter-proton distances and the intensities is given by the
exponential function:
aCt=a) = exp(-RCm) ;
where R is the relaxation matrix. The off-diagonal elements of the relaxation matrix are propor-
tional to I/rij6 •
Rij - 0.l,yi2 7j 21~[6J(o~ i + ~j) - J((0 i - ¢~j)] / rij6.
Thus, for short mixing times (Zm---~), the inter-proton d i ~ can be estimated from the cross-
peak intensities. At longer mixing limes this approximation breaks down due to spin diffusion.
However, it is with mixing times of intermediate duration where one begins to observe a reason-
able number of cross-peaks with acceptable signal/noise.
In contrast to the approximate approach, exact intensities can be calculated for a given
three-dimensional array of pmtom after diagonalizing the relaxation matrix:
= exp(- ;
where ;L is the diagonal eigenvalue matrix and ~ is the associated matrix of eigenveaors? We
have incorporated this exact calculation of intensifies into a least-squares program which refines
oligonucleotide structure. In the course of this work we have investigated the consequences of
errors in the data on the refinement process. The major conclusions to be drawn are the foUowing.
(1) ConsWaints are necessary. Refinement of the proton "smmure" in 3-space, without con-
straints due to the molecular skeleton, is unsuccessful. In our approach each nucleotide
is defined by ten parameters: 3 translational coordinates and 3 Euler angles for the whole
nucleotide, 2 internal torsion angles (the glycosidic and C4'--C5' bonds) and the sugar
pucker phase and amplitude. The phosphodiester linkages are not included.
(2) Errors in diagonal peak intensifies (easily approaching 50% in the case of overlap) utterly
destroy the refinement if they are included in calculation of the residuals. However, if
the diagonals are ignored completely, the refinement is successful.
(3) The correlation times can be successfully refined.
References
(1) Kline, A. D.; Braun, W.; Wfithrich, K. J. Mol. Biol. (1986) 189, 377-382.
(2) Clore, G. M.; Gronenbom, A. M.; Brfinger, A. T.; Karplus, M. J. Mol. Biol. (1985) 186,435-455.
(3) Keepers, J. W., James, T. I.. J. Magn. Reson. (1984) $7, 404-426.